Internal problem ID [6618]
Book: First order enumerated odes
Section: section 1
Problem number: 55.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\frac {1}{x y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 43
dsolve(diff(y(x),x)^2=1/(y(x)*x),y(x), singsol=all)
\begin{align*} \frac {\left (x y \relax (x )\right )^{\frac {3}{2}}}{x^{\frac {3}{2}}}-3 \sqrt {x}-c_{1} = 0 \\ \frac {\left (x y \relax (x )\right )^{\frac {3}{2}}}{x^{\frac {3}{2}}}+3 \sqrt {x}-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.919 (sec). Leaf size: 53
DSolve[(y'[x])^2==1/(y[x]*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (-2 \sqrt {x}+c_1\right ){}^{2/3} \\ y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (2 \sqrt {x}+c_1\right ){}^{2/3} \\ \end{align*}